In this example there is an inflow of 50 "*" units per generation. There also is a loss of X% of the population each generation (the outflow.) An equilibrium will be attained when the two are equal (i.e. the inflow and outflow are in balance.)

This equilibrium can be calculated, or it can be visualized using the following demonstration.

Select the % loss and initial population size. Then click Setup. After each click of the Go One Generation button, the display shows the resulting population.

	Select the % loss: 5% 10% 20% Select the initial population size: 1 100 200 300 400 500 600 700 800 900 1000
	Last Generation Count: This Generation Count: Generation Number:

• Does the initial population size have any effect on the equilibrium size reached?
• What does affect the equilibrium size?
• For what parameter combinations does it take a longer/shorter time to approach equilibrium?
• When, for any set of parameters, is the approach faster, when is it slower?
• How could one calculate the equilibrium size algebraically? Note: X is the %loss, and N is the population size (the inflow is fixed at 50.)
  • What is the loss in one generation?
    • Hint: To multiply by a %, divide it by 100 (i.e. change it to decimal fraction) before proceeding.
  • What is the inflow each generation?
  • What is the change in population size in one generation?
  • What is the relationship between the loss and inflow at equilibrium?
  • Write the equation showing this relationship.
• What does it mean to approach equilibrium "from above" or "from below"?
  • Can you illustrate this using the exercise above?
• The inflow in this exercise is fixed at 50 per generation.
  • Does this limit the demonstration of populations size equilibrium?
    Hint: Is it the amount of inflow, or the ratio of inflow to other parameters which determines the equilibrium size?
• The outflow in this model is chosen to be a % of the amount in the compartment. So it is a "linear function" of the amount.
  • Could other functions be chosen?
  • Advanced Question: Are there functions which would keep the compartment from reaching an equilibrium value?